FROM NEW FUNDAMENTAL EQUATION OF STATISTICAL PHYSICS TO THE FORMULA FOR ENTROPY PRODUCTION RATE

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2432-2440 ◽  
Author(s):  
XIU-SAN XING
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Statistical Physics ◽  
Classical Mechanics ◽  
Fundamental Equation ◽  
Entropy Production Rate ◽  
Unified Framework ◽  
Nonequilibrium States ◽  
The Difference ◽  
Thermodynamic Processes

Why the classical mechanics and quantum mechanics are reversible while the macroscopic thermodynamic processes are irreversible? Is it because both of the two are different fundamental laws? If yes, what is the difference between them? What is the fundamental equation of nonequilibrium statistical physics? Can it provide a unified framework of statistical physics including nonequilibrium states and equilibrium states? How can we derive rigorously the hydrodynamic equations from microscopic kinetics? Does nonequilibrium entropy obey any evolution equation? What is the form of this equation if it exist? What is the microscopic physical basis of entropy production rate namely the law of entropy increase? Can it be described by a quantitative concise formula? What mechanism is responsible for the processes of approach to equlibrium? How to quantitatively describe it? In this paper we try to solve all these problems from a new fundamental equation of statistical physics in a unified fasion.

Entropy Production in Oscillating Chemical Systems

1985 ◽  
Vol 40 (9) ◽  
pp. 877-884 ◽  
Author(s):  
Bengt Å. G. Månsson
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Mass Action ◽  
Entropy Production Rate ◽  
Stationary States ◽  
Control Parameters ◽  
Mass Action Kinetics ◽  
Chemical Systems ◽  
Stable Periodic ◽  
The Difference

Abstract The entropy production in oscillating homogenous chemical systems is investigated by analyzing the difference between the average entropy production rate in a stable periodic oscillatory mode and in the corresponding unstable stationary state. A general analytical expression for this difference in the neighborhood of a Hopf bifurcation is derived. The entropy production in two typical models of chemical systems with unstable stationary states and stable periodic oscillations is investigated, using fixed concentrations as control parameters. The models exemplify both positive and negative entropy production rate differences. One of the investigated models has four free concentrations, the other three. The rate expressions are given by second order mass action kinetics with reverse reactions taken into account. The flows of reactants and products are controlled so that only the free concentrations vary, and the entropy of mixing associated with these flows is discussed.

scholarly journals Entropy Production Rate for Avascular Tumor Growth

2011 ◽  
Vol 02 (06) ◽  
pp. 615-620 ◽  
Author(s):  
Elena Izquierdo-Kulich ◽  
Esther Alonso-Becerra ◽  
José M Nieto-Villar
Keyword(s):  
Tumor Growth ◽  
Entropy Production ◽  
Production Rate ◽  
Entropy Production Rate ◽  
Avascular Tumor

scholarly journals Measurement of entropy production rate in compressible turbulence

2006 ◽  
Vol 76 (4) ◽  
pp. 595-601 ◽  
Author(s):  
M. M Bandi ◽  
W. I Goldburg ◽  
J. R Cressman
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Compressible Turbulence ◽  
Entropy Production Rate

scholarly journals Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 881 ◽  
Author(s):  
Karl Hoffmann ◽  
Kathrin Kulmus ◽  
Christopher Essex ◽  
Janett Prehl
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Irreversible Processes ◽  
Entropy Production Rate ◽  
Continuous Space ◽  
One Dimensional ◽  
Fractional Diffusion Equations ◽  
And Diffusion

The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a finite chain of points described by a fractional master equation.

scholarly journals Testing the Steady-State Fluctuation Relation in the Solar Photospheric Convection

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 716
Author(s):  
Giorgio Viavattene ◽  
Giuseppe Consolini ◽  
Luca Giovannelli ◽  
Francesco Berrilli ◽  
Dario Del Moro ◽  
...  
Keyword(s):  
Steady State ◽  
Entropy Production ◽  
Production Rate ◽  
Local Level ◽  
Entropy Production Rate ◽  
Quasi Steady State ◽  
The Sun ◽  
Statistical Features ◽  
Local Entropy ◽  
Fluctuation Relation

The turbulent thermal convection on the Sun is an example of an irreversible non-equilibrium phenomenon in a quasi-steady state characterized by a continuous entropy production rate. Here, the statistical features of a proxy of the local entropy production rate, in solar quiet regions at different timescales, are investigated and compared with the symmetry conjecture of the steady-state fluctuation theorem by Gallavotti and Cohen. Our results show that solar turbulent convection satisfies the symmetries predicted by the fluctuation relation of the Gallavotti and Cohen theorem at a local level.

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